Sazerac Cocktail History at the What's Cooking America makes little notice of the absinthe, discussing the history involving Peychaud. As I read it, "patent medicine" usually involved some drug (opioid, coca extract) we can't accurately replicate:
The Sazerac cocktail is to New Orleans what the margarita is to the southwest. It is reported to be the first cocktail every invented (at least in the United States). Antoine Amadie Peychaud, a Creole apothecary, is given the credit for first inventing the Sazerac cocktail in the 1830s. In 1795, he immigrated to New Orleans from the West Indies and opened a drugstore called Pharmacie Peychaud. Like many "chemists" of his day, he sold his own patent medicine; Peychaud's Bitters, a proprietary mix of aromatic bitters said to relive his clients' ailments. His medical toddy soon became very popular and friends gathered regularly to sample his late-night drinks.Also see Liqueurs de France's note on the Sazerac, specifically the "Cognac Sazerac-de-Forge."